Orx supports multiple monitors. You can open your game on any chosen monitor by using the Monitor property of the Display section.
[Display] Monitor = 2
This will open your game on the second monitor, not your main one.
If you specify monitor = 2 or greater than one, and you only have a single monitor, Orx will revert to monitor 1, and quietly warn you in the log output with:
Invalid monitor: index [2] out of range, max is [1]. Reverting to current monitor.
In the Orx console, you can get the current monitor that your Orx application is running on:
get Display Monitor
This is works in either windowed or fullscreen modes.
Also, if you drag your game window to your second monitor, and toggle to fullscreen mode, the fullscreen will stay on that monitor.